function euler_method

nn=5;                %initial number of subintervals
%exact=atan(x)       %exact solutions
%f=1/(1+tan(x)^2);

for m=1:5
    n=nn*2^(m-1);    %number of subintervals
    e=zeros(n+1);
    h=5/n;           %step size
    t=0:h:5;
    for i=1:n
        %e(i+1)=e(i)+h*subs(f,x,e(i));
        e(i+1)=e(i)+h*f(e(i)); %carrying out Euler method
    end
    y=exact(t);
    %y=subs(exact,x,t);
    error(m)=abs(y(n+1)-e(n+1));%error at t=5
    plot(t,e);
    hold on;
end


plot(t,y,'r');
error
for m=1:4
    ratio(m)=error(m)/error(m+1);
end
ratio

function d=f(x)
d=1/(1+tan(x)^2);

function d=exact(x)
d=atan(x);